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Computing the degreewidth of a digraph is hard

par Aboulker, Pierre ;Oijid, Nacim;Petit, Robin ;Rocton, Mathis;Simon, Christopher-Lloyd
Référence Discrete mathematics and theoretical computer science, 28, 2, 15
Publication Publié, 2026-04-09

Article révisé par les pairs

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Résumé :

Given a digraph, an ordering of its vertices defines a backedge graph, namely the undirected graph whose edges correspond to the arcs pointing backwards with respect to the order. The degreewidth of a digraph is the minimum over all ordering of the maximum degree of the backedge graph. We answer an open question by Keeney and Lokshtanov [WG 2024], proving that it is NP-hard to determine whether an oriented graph has degreewidth at most 1, which settles the last open case for oriented graphs. We complement this result with a general discussion on parameters defined using backedge graphs and their relations to classical parameters.